Kerfing is forming a groove in the gemstone, which is done prior to cleaving; cleaving is parting a gemstone along a cleavage plane. There is a description of kerfing and cleaving in "Diamonds", by Eric Bruton, 2nd edition, 1978, NAG Press, London.
It will be understood that working a gemstone with a laser normally involves material removal, though in thermal cleaving the stone may be split along the cleavage plane without any material being removed.
The present description relates specifically to diamonds, but it is believed that it is generally applicable to other gemstones although some of the effects may be markedly different, such as in diamonds the presence of clear cleavage planes, the formation of graphite and the resulting higher absorption of energy, and the higher thermal and mechanical strength.
Working gemstones with lasers is found to give a combination of particular problems which is not met with when working other materials. For instance, the gemstones in general have a very low absorption of the laser energy, giving problems in reaching the working temperature; wastage of the gemstone must be kept very low due to the value of the gemstone material; likewise, a clean cut reduces later wastage of gemstone material; and chipping and subsequent blowing off of pieces of the gemstone can occur and can be very wasteful.
Furthermore, kerfing gemstones requires special measures in that a line must be cut, which is more difficult than machining a spot, and the line must have a cross-sectional shape suitable for a subsequent cleaving operation.